Thus, it's odd that Butterfield listed these two problems and not the vastly more important problem that the Standard Model and GR can't both be correct. We know we need to tweak one or both of these theories to get a consistent framework that fits the data we have!
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Replying to @johncarlosbaez @skdh
To understand this more precisely, can we say something stronger, such as that GR is actually wrong at small scales -- that is, conflicts with experiment rather than just with the Standard Model? And is there any large-scale phenomenon that the Standard Model gets wrong?
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The Standard Model, taken seriously at large scales, predicts that there is no gravity. General relativity, taken seriously at small scales, says that atoms don't have quantized energy levels. So, nobody takes them seriously in these realms they weren't designed for.
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The fundamental problem is that general relativity and quantum mechanics are not just physical theories; each is a comprehensive conceptual framework that imposes constraints on all possible physical theories -- and each ignores the constraints of the other.
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Replying to @MathPrinceps @johncarlosbaez and
Quantum mechanics presumes a classical theory of spacetime. One cannot even enunciate its basic structural laws without one. But the classical theory of spacetime it presumes is obviously the wrong one; its empirical inadequacies are spectacular. So what to do?
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Replying to @MathPrinceps @johncarlosbaez and
Should one "quantize general relativity," or "general-relativize" quantum theory? Or perhaps do neither? Or both? Some argue that "quantizing" space and time is wrong-headed -- like replacing thermodynamic temperature by a self-adjoint operator on some Hilbert space of states.
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Replying to @MathPrinceps @johncarlosbaez and
And as for "general-relativizing" quantum theory, this seems at best a distant dream beset by formidable obstacles both technical and conceptual. Indeed, one can still win a million dollars, and lasting global fame, merely by "special-relativizing" quantum theory.
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Replying to @MathPrinceps @johncarlosbaez and
Meantime, it remains unclear whether any experiment can ever be done by humans that might reveal some essential predictive inadequacy in either general relativity or quantum theory. Each, supreme in its own domain and haughtily ignoring the other, seems all but invulnerable.
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Replying to @MathPrinceps @johncarlosbaez and
So the situation is perhaps about as discouraging as it could possibly be. We know we're wrong, yet we lack access to phenomena capable of forcing us to correct our errors (and of guiding our guesswork as we struggle to correct them.)
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I'm actually pretty optimistic that we'll solve this; it's hard to combine the insights of quantum theory and general relativity, but that very difficulty is helpful, because it provides a strong constraint in a situation where we don't have enough experiments. (continued)
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This is the same brash optimism ruggedly clung to throughout a long and vigorous life by the late, great Bryce Seligman DeWitt.
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Replying to @MathPrinceps @johncarlosbaez and
Alas, though he is arguably the Moses of quantum gravity, it was not given unto him even to see into the Promised Land.
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